Abstract

A spatiotemporal approach for fast absolute shape measurements is formulated. In principle, the Takeda method is used in combination with the reduced temporal phase-unwrapping scheme to calculate the absolute phase. Three different measurements are performed: a flat surface, steps, and a curved beam with varying cross sections. The performance in standard deviation is improved, and the success rate is approximately the same as that obtained with a strict temporal solution for which a four-bucket phase algorithm is used. The multichannel approach is also used. Then only one static image is needed. It should therefore be possible to measure objects in motion.

© 2004 Optical Society of America

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References

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  1. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  2. J. M. Huntley, H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
    [CrossRef] [PubMed]
  3. H. Zhao, W. Chen, Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33, 4497–4500 (1994).
    [CrossRef] [PubMed]
  4. J. M. Huntley, H. O. Saldner, “Error-reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. 14, 3188–3196 (1997).
    [CrossRef]
  5. H. O. Saldner, J. M. Huntley, “Temporal phase unwrapping: Application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
    [CrossRef] [PubMed]
  6. H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610–615 (1997).
    [CrossRef]
  7. J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping: Comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986–992 (1997).
    [CrossRef]
  8. J. M. Huntley, C. R. Coggrave, “Progress in phase unwrapping,” in International Conference on Applied Optical Metrology, K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 86–93 (1998).
    [CrossRef]
  9. L. Kinell, M. Sjödahl, “Robustness of reduced temporal phase unwrapping in the measurement of shape,” Appl. Opt. 40, 2297–2303 (2001).
    [CrossRef]
  10. L. Kinell, “Multichannel method for absolute shape measurement using projected fringes,” Opt. Lasers Eng. 41, 57–71 (2004).
    [CrossRef]
  11. L. Kinell, M. Eriksson, M. Sjödahl, “Component forming simulations validated using optical shape measurements,” in Optical Measurement Systems for Industrial Inspection III, W. Oster, M. Kujawinska, K. Creath, eds., Proc. SPIE5144, 409–419 (2003).
    [CrossRef]
  12. P. S. Huang, Q. Ho, F. Jin, F. P. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3D surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
    [CrossRef]
  13. R. G. Dorsch, G. Häusler, J. M. Herrmann, “Laser triangulation: Fundamental uncertainty in distance measurement,” Appl. Opt. 33, 1306–1314 (1994).
    [CrossRef] [PubMed]
  14. G. H. Notni, G. Notni, “Digital fringe projection in 3D shape measurement—an error analysis,” in Optical Measurement Systems for Industrial Inspection III, W. Oster, M. Kujawinska, K. Creath, eds., Proc. SPIE5144, 372–380 (2003).
    [CrossRef]
  15. J. Burke, H. Helmers, “Complex division as a common basis for calculating phase differences in electronic speckle pattern interferometry in one step,” Appl. Opt. 37, 2589–2590 (1998).
    [CrossRef]

2004

L. Kinell, “Multichannel method for absolute shape measurement using projected fringes,” Opt. Lasers Eng. 41, 57–71 (2004).
[CrossRef]

2001

1999

P. S. Huang, Q. Ho, F. Jin, F. P. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3D surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

1998

1997

H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610–615 (1997).
[CrossRef]

J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping: Comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986–992 (1997).
[CrossRef]

J. M. Huntley, H. O. Saldner, “Error-reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. 14, 3188–3196 (1997).
[CrossRef]

H. O. Saldner, J. M. Huntley, “Temporal phase unwrapping: Application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
[CrossRef] [PubMed]

1994

1993

1982

Burke, J.

Chen, W.

Chiang, F. P.

P. S. Huang, Q. Ho, F. Jin, F. P. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3D surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Coggrave, C. R.

J. M. Huntley, C. R. Coggrave, “Progress in phase unwrapping,” in International Conference on Applied Optical Metrology, K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 86–93 (1998).
[CrossRef]

Dorsch, R. G.

Eriksson, M.

L. Kinell, M. Eriksson, M. Sjödahl, “Component forming simulations validated using optical shape measurements,” in Optical Measurement Systems for Industrial Inspection III, W. Oster, M. Kujawinska, K. Creath, eds., Proc. SPIE5144, 409–419 (2003).
[CrossRef]

Häusler, G.

Helmers, H.

Herrmann, J. M.

Ho, Q.

P. S. Huang, Q. Ho, F. Jin, F. P. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3D surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Huang, P. S.

P. S. Huang, Q. Ho, F. Jin, F. P. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3D surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Huntley, J. M.

J. M. Huntley, H. O. Saldner, “Error-reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. 14, 3188–3196 (1997).
[CrossRef]

H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610–615 (1997).
[CrossRef]

H. O. Saldner, J. M. Huntley, “Temporal phase unwrapping: Application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
[CrossRef] [PubMed]

J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping: Comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986–992 (1997).
[CrossRef]

J. M. Huntley, H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
[CrossRef] [PubMed]

J. M. Huntley, C. R. Coggrave, “Progress in phase unwrapping,” in International Conference on Applied Optical Metrology, K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 86–93 (1998).
[CrossRef]

Ina, H.

Jin, F.

P. S. Huang, Q. Ho, F. Jin, F. P. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3D surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Kinell, L.

L. Kinell, “Multichannel method for absolute shape measurement using projected fringes,” Opt. Lasers Eng. 41, 57–71 (2004).
[CrossRef]

L. Kinell, M. Sjödahl, “Robustness of reduced temporal phase unwrapping in the measurement of shape,” Appl. Opt. 40, 2297–2303 (2001).
[CrossRef]

L. Kinell, M. Eriksson, M. Sjödahl, “Component forming simulations validated using optical shape measurements,” in Optical Measurement Systems for Industrial Inspection III, W. Oster, M. Kujawinska, K. Creath, eds., Proc. SPIE5144, 409–419 (2003).
[CrossRef]

Kobayashi, S.

Notni, G.

G. H. Notni, G. Notni, “Digital fringe projection in 3D shape measurement—an error analysis,” in Optical Measurement Systems for Industrial Inspection III, W. Oster, M. Kujawinska, K. Creath, eds., Proc. SPIE5144, 372–380 (2003).
[CrossRef]

Notni, G. H.

G. H. Notni, G. Notni, “Digital fringe projection in 3D shape measurement—an error analysis,” in Optical Measurement Systems for Industrial Inspection III, W. Oster, M. Kujawinska, K. Creath, eds., Proc. SPIE5144, 372–380 (2003).
[CrossRef]

Saldner, H.

Saldner, H. O.

J. M. Huntley, H. O. Saldner, “Error-reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. 14, 3188–3196 (1997).
[CrossRef]

H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610–615 (1997).
[CrossRef]

J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping: Comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986–992 (1997).
[CrossRef]

H. O. Saldner, J. M. Huntley, “Temporal phase unwrapping: Application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
[CrossRef] [PubMed]

Sjödahl, M.

L. Kinell, M. Sjödahl, “Robustness of reduced temporal phase unwrapping in the measurement of shape,” Appl. Opt. 40, 2297–2303 (2001).
[CrossRef]

L. Kinell, M. Eriksson, M. Sjödahl, “Component forming simulations validated using optical shape measurements,” in Optical Measurement Systems for Industrial Inspection III, W. Oster, M. Kujawinska, K. Creath, eds., Proc. SPIE5144, 409–419 (2003).
[CrossRef]

Takeda, M.

Tan, Y.

Zhao, H.

Appl. Opt.

J. Opt. Soc. Am.

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
[CrossRef]

J. M. Huntley, H. O. Saldner, “Error-reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. 14, 3188–3196 (1997).
[CrossRef]

Meas. Sci. Technol.

J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping: Comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986–992 (1997).
[CrossRef]

Opt. Eng.

H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector,” Opt. Eng. 36, 610–615 (1997).
[CrossRef]

P. S. Huang, Q. Ho, F. Jin, F. P. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3D surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Opt. Lasers Eng.

L. Kinell, “Multichannel method for absolute shape measurement using projected fringes,” Opt. Lasers Eng. 41, 57–71 (2004).
[CrossRef]

Other

L. Kinell, M. Eriksson, M. Sjödahl, “Component forming simulations validated using optical shape measurements,” in Optical Measurement Systems for Industrial Inspection III, W. Oster, M. Kujawinska, K. Creath, eds., Proc. SPIE5144, 409–419 (2003).
[CrossRef]

G. H. Notni, G. Notni, “Digital fringe projection in 3D shape measurement—an error analysis,” in Optical Measurement Systems for Industrial Inspection III, W. Oster, M. Kujawinska, K. Creath, eds., Proc. SPIE5144, 372–380 (2003).
[CrossRef]

J. M. Huntley, C. R. Coggrave, “Progress in phase unwrapping,” in International Conference on Applied Optical Metrology, K. Rastogi, F. Gyimesi, eds., Proc. SPIE3407, 86–93 (1998).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Setup for measuring the shape of an object within the measurement volume by use of active triangulation. The system consists of a color-video projector, with three LCDs for projection and a CCD camera for acquisition of images.

Fig. 2
Fig. 2

Basic principle of temporal phase unwrapping. The straight line shows the constant increase in phase in a given pixel as a function of the number of projected fringes. Marked with circles is the negative exponential sequence with 8, 12, 14, 15, and 16 fringes. The filled circles correspond to the reduced temporal phase-unwrapping sequence with three fringe densities.

Fig. 3
Fig. 3

Standard deviation results of phase (ω+) and shape (Z) (a), (b) across and (c), (d) along the fringes from a measured flat surface. To the left, in (a) and (c), are the results from using the four-bucket algorithm combined with the reduced temporal phase-unwrapping scheme. Corresponding results are shown in (b) and (d), in which the Takeda method is combined with the reduced temporal phase-unwrapping scheme. Presented results are calculated from images by a full negative-exponential sequence, starting at 128 fringes. The figure shows the calculated phase with a subtracted phase plane for a section across the fringes, denoted as ω+ and plotted as solid curves. The curvature of the curve is derived from the triangulation angle and the distortion of the optical system. In (a)–(d), the corresponding calibrated result Z for each pixel is indicated by dashed curves.

Fig. 4
Fig. 4

Success rate (S.R.) and standard deviation (Std) for various fringe sequences. The same plane as that in Fig. 3 is measured. The results plotted with circles are calculated with the four-bucket algorithm combined with the reduced temporal phase-unwrapping scheme. Corresponding results from using the Takeda method with the reduced temporal phase-unwrapping scheme are plotted with crosses. In (a) a reduced exponential sequence starting with s = 64 fringes is used, and in (b) a sequence starting with s = 128 fringes is used. Results connected by dotted curves are standard deviation, and those connected with dashed curves are success rate. A fringe sequence length of m = 2 corresponds to the fringe sequence 63, 64 in (a) and 127, 128 in (b).

Fig. 5
Fig. 5

Measurement results of three flat isolated surfaces: (a) surfaces with a fringe pattern covering the whole field of view; (b) the phase calculated with the Takeda method combined with the reduced temporal phase-unwrapping method. The sequence used is s = 64 and m = 3 (62, 63 and 64 fringes). The profile in (c) and the mesh in (d) are the shapes, or 3-D coordinates, of the measured surfaces.

Fig. 6
Fig. 6

Screen shot from the measurement system built up during a shape measurement of the beam.

Fig. 7
Fig. 7

Measurement results of the beam obtained with the four-bucket algorithm in combination with the reduced temporal phase-unwrapping scheme. The results are calculated from a sequence of (a) 48, 56, 60, 62, 63, 64 fringes; (b) of 62, 63, 64 fringes; (c) 63, 64 fringes. Instead of the results obtained with gray-scale fringes as in (a)–(c), the results in (d) are calculated with the same sequence as that used in (c) but with green channel allowed to carry 63 fringes and the blue channel allowed to carry 64 fringes.

Fig. 8
Fig. 8

Results in (a)–(d) are calculated with the same data and fringe sequences as those of Fig. 7, but with the reduced temporal phase-unwrapping scheme used in combination with Takeda method. The results in this figure are therefore directly comparable with those of Fig. 7.

Tables (1)

Tables Icon

Table 1 Fringe Sequences Used in the Measurements

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

gx, y=ax, y+bx, ycos2πf0x+ϕx, y,
gx, y=ax, y+cx, yexpi2πf0x+c*x, yexp-2πf0x,
cx, y=12 bx, yexpiϕx, y.
Gx, y=Afx, y+Cfx-f0, y+C*fx+f0, y,
ϕw=tan-1Imcx, yRecx, y,
bx, y=Imcx, y2+Recx, y21/2.
t=2k-1, s,
Δϕus-ti, s-ti+1=UΔϕw×s-ti, s-ti+1, Δϕus, s-ti,
Δϕus, s-ti+1=Δϕus, s-ti+Δϕu×s-ti, s-ti+1,
Uϕ1, ϕ2=ϕ1-2π NINTϕ1-Tϕ22π,
ωˆ=sϕus+i=1m-1s-tiϕus-tis2+i=1m-1s-ti2,

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